5 Answers
5

Because they aren't specifically the same thing. While they share a similar abilities (the power to alter the environment around them, and the generation of colossal amounts of energy) the Tesseract in the Marvel Cinematic Universe is essentially a doorway through space (and possibly time), the Cosmic Cube is an object of immense power that has several vaguely defined abilities. They both can be associated with the mad Titan Thanos and the Red Skull in both universes. The fact that Marvel Studios chose not to explicitly refer to the object depicted in Thor, Captain America: The First Avenger, and Avengers as "The Cosmic Cube" allows for them to use that name to describe another cube if they chose to show A.I.M. creating one in a later movie.

In Thor: The Dark World, it's revealed that the Tesseract is in fact one of the Infinity Gems. Something they were able to do because they previously avoided calling it a Cosmic Cube.

You say the Tesseract is a doorway and Cube is "an object of immense power," but clearly the Tesseract is also an object of power. In Captain America: The First Avenger, for instance, that's precisely what we see---the Tesseract was a power source, in that case being use to power futuristic Hydra weapons. So it's a doorway AND "an object of immense power" like the Cube.
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FoxMan2099Nov 8 '13 at 21:51

@FoxMan2099 Being a doorway was it's primary function, the fact that it boasted immense power was incidental. The Cosmic Cube's main function was to reshape reality to it's masters whims.
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Monty129Nov 8 '13 at 21:56

Incidental? That's the danger that drives the plot of The First Avenger---the Red Skull can power futuristic weapons with the Tesseract/Cube.
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FoxMan2099Nov 9 '13 at 2:34

If you had a reality bending energy wouldn't that essentially be capable of creating a doorway anyway? So what's the difference between the two? Personally I think they are literally the same thing just with different names. Albeit it some minor differences as it's considered one of the infinity gems in the marvel cinematic universe.
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DoctorWho22Jun 30 '14 at 13:49

The Chitauri are a fictional race of extraterrestrial shapeshifters
that appear in publications by Marvel Comics's alternative universe,
Ultimate Marvel, in the limited series The Ultimates. They were
created by Mark Millar and Bryan Hitch. They were created for the
Ultimate universe franchise in place of the existing Marvel Comics
alien species, the Skrulls, which play a similar role in the
franchise's mainstream continuity. Later, Marvel would choose to
distinguish between the Skrulls and Chitauri of the Ultimate universe.
The species would later be adapted to other media, notably appearing
in the 2012 film The Avengers as an invasion force led by Loki.

All of that merely shows that there are several different universes in the Marvel Multiverse. In the movie, we were simply in a different reality (namely earth-199999). There's no real reason to even expect that the cube is a Cosmic Cube.

The Cosmic Cube or Tesseract, as it is mostly called, of this reality
is a powerful Asgardian artifact created by Odin which possesses the
abilities to create infinite energy, which can be used to create
wormholes to other parts of the universe and different dimensions,
rather than reality manipulation. Unknowngly why, the Tesseract was
hidden on Earth.

This needs to be edited to tie it back to the posed question.
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Keen♦Mar 14 '13 at 14:59

@Keen - you're right, so I added supporting documentation to show that my original answer - that the name is different is because it's from an alternate reality to the main timeline - was correct, straight from a Canon source.
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David StrattonMar 31 '13 at 2:09

Marvel cinematic universe is different from existing marvel-comic-verse. So Tesseract is a Infinity Gem which look inspired from cosmic cube. Even Thanos end credit scene make more sense now because his comic counterpart want to have all six infinity gems for a big purpose.

If, in fact, the Tesseract is the cosmic cube appearing in Marvel comics, then the Thanos character would only need to acquire this artifact from Loki and his desires would likely be fulfilled. He would not need to send the "other" to enlist Loki's aid to conquer Earth, the cube would accomplish this task quite easily. This cube, the Tesseract, is very powerful as a source of unlimited energy, but it is not useful as a complete weapon in itself.

In the marvel movie verse many things are changed simply because they are to complicated to do in a movie, e.g. Explaining how the cube was made as well as it being to powerful an enemy for the Avengers to battle. Especially in their first team up.